A time- and temperature-dependent viscoelastic model based on the statistical compatibility condition

Abstract

This paper presents a novel methodology to characterize viscoelastic materials, allowing the limitations of current conventional models based on Time-Temperature-Superposition (TTS) principle to be avoided. It implies the definition of the temperature-time field, T-t, from short-term recorded relaxation curves at different temperatures by establishing the compatibility condition between the temperature dependent relaxation modulus at given time, E(T;t), and the time dependent relaxation modulus for a given temperature, E(t;T). The solution of the resulting functional equation allows the T-t field to be analytically defined by assuming the normalized relaxation function to be a stochastic model properly identified as a survival cumulative distribution function of certain statistical families such as normal or Gumbel ones. As a result, the corresponding master curves in the T-t field for both E-t and E-T functions are directly derived over the whole range of time and temperature, preventing user's influence on the definition of the classical shift factors and the minimum overlapping requirement over time on the short-term curves. The suitability of the proposed methodology is confirmed by its application to the experimental results from a campaign of relaxation tests on commercial PVB (polyvinyl butyral) at different temperatures.

Keywords

• Viscoelastic behaviour
• Relaxation curves
• Master curve
• Gumbel distribution
• Time-temperature superposition principle